Apply the Distance &
Midpoint formulas
Find the distance and the midpoint
Find the missing endpoint
Formulas:
Distance formula:
d  ( x2  x1 )  ( y2  y1 )
2
2
Midpoint formula:
x2  x1
 xmidpoint
2
y2  y1
 ymidpoint
2
( xmidpoint , ymidpoint )
Ex 1
( x1, y1 )
( x2, y2 )
Find the distance between the points P(-3, 2) and Q (-2, 4).
d  ( x2  x1 )  ( y2  y1 )
2
d  (2  3 )  (
2
d (
1
) (
d
d
2
1

5
4
4
2
2
 2)
)
2
2
Work inside
parentheses
Do powers before
doing the
addition!!!!!!
Ex 2
( x1, y1 )
( x2, y2 )
Find the distance between the points P(-5, 3) and Q (4, 5).
d  ( x2  x1 )  ( y2  y1 )
2
d  ( 4  5 )  (
2
d (
9
d
d
) (
2
81  4
85
5
2
2
 3)
)
2
2
Work inside
parentheses
Do powers before
doing the
addition!!!!!!
Ex 3
( x1, y1 )
( x2, y2 )
Find the distance between the points P(-2, -5) and Q (-1, 3).
d  ( x2  x1 )  ( y2  y1 )
2
d  ( 1  2 )  (
2
d (
1
d
d
3
) (
2
1
 64
65
8
2
 5)
)
2
2
Work inside
parentheses
Do powers before
doing the
addition!!!!!!
Ex 4
( x2, y2 )
( x1, y1 )
Find the midpoint whose endpoints are (2, -3) and (-14, 13)
x2  x1
 xmidpoint
2
14  2
 xmidpoint
2
12
2

y2  y1
 ymidpoint
2
13

2
3
10
6
2
 ymidpoint

(6 , 5 )
( xmidpoint , ymidpoint )
5
Ex 5
( x2, y2 )
( x1, y1 )
Find the midpoint whose endpoints are (1, -2) and (-17, 16)
x2  x1
 xmidpoint
2
17  1
 xmidpoint
2
16
2

8
y2  y1
 ymidpoint
2
16  2
 ymidpoint
2
14
2

(8 , 7 )
( xmidpoint , ymidpoint )
7
Ex 6M(-3, -5) is the midpoint of RS.
If S has a coordinates (-2, 2),
find the coordinates of R.
( x1, y1 )
R (x1, y1)
(2)
2 x1
2
( x2, y2 )
( xm , ym )
M(-3, -5)
S (-2, 2)
2  y1
3 (2) (2)
2  x1  6
2
2
2
 5 (2)
2  y1  10
2
x1  4
(4 ,12)
2
y1  12
7 ExM(4, 2) is the midpoint of RS.
If S has a coordinates (5, -2),
find the coordinates of R.
( x1, y1 )
R (x1, y1)
x1

5
(2)
2
5  x1 
5
( xm , ym )
( x2, y2 )
M(4, 2)
S (5,-2)
 4 (2) (2)
2

2
y1
 2 (2)
2  y1  4
8
5
2
x1  3
(3 ,
6
)
2
y1  6
Ex 8
M(-8, 7) is the midpoint of RS. If S has a coordinates (-6, 8),
find the coordinates of R.
( x1, y1 )
R (x1, y1)
x1


6
(2)
2
( x2, y2 )
( xm , ym )
M(-8, 7)
8 (2)
S (-6, 8)
y1

8
(2)
 7 (2)
2
8  y1  14
6  x1  16
6
6
8
x1  10
(10 ,
6
)
8
y1  6